Question: The grades on a math midterm at Santa Rita are normally distributed with $\mu = 80$ and $\sigma = 2.5$. Vanessa earned a $77$ on the exam. Find the z-score for Vanessa's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Vanessa's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{77 - {80}}{{2.5}}} $ ${ z \approx -1.20}$ The z-score is $-1.20$. In other words, Vanessa's score was $1.20$ standard deviations below the mean.